Analysis of Entropy Generation Minimization during Natural Convection in Trapezoidal Enclosures of Various Angles with Linearly Heated Side Wall(s)

Entropy generation during natural convection in trapezoidal enclosures with various inclination angles (psi) = phi 45 degrees, 60 degrees, and 90 degrees for uniformly heated bottom wall and insulated top wall with linearly heated side walls (case 1) or linearly heated left wall with cold right wall (case 2) have been investigated numerically using penalty finite element method. Parametric studies for the wide range of Rayleigh numbers (Ra = 10(3)-10(5)) and Prandtl numbers (Pr = 0.015-1000) have been performed. Symmetry in flow pattern is observed for case 1. During the conduction regime at low Ra (Ra = 10(3)), the entropy generation in the cavity is dominated by heat transfer irreversibility for all Pr. The strength of fluid flow increases with Ra and that leads to an increase in thermal energy transport due to enhanced convection at Ra = 10(5). Consequently, the entropy generation due to heat transfer (S-theta) and fluid friction (S-psi) also increases with Ra for all Pr. The comparison of magnitudes of S-theta and S-psi, indicates that maximum entropy generation due to heat transfer (S-theta,S-max) and fluid friction (S psi(,max)) is lower for case 1 and higher for case 2. It is found that (S-theta,S-max) x occurs at the top portion of side walls in case 1, whereas S-theta,S-max occurs at a hot-cold junction due to a high thermal gradient in case 2. The total entropy generation, S-total is found to be smaller in case 1 and larger in case 2 for all Pr at Ra = 10(5). It is observed that 5 occurs at the top wall in both heating situations for Pr = 0.015 and Ra = 10(5). It is also found that, S-psi,S-max is observed near side walls in case 1, whereas that is observed near the right cold wall in case 2 for Pr = 0.7 and 1000 at Ra = 10(5). The total entropy generation (S-total) is larger for psi = 45 degrees in both heating cases at high Pr (Pr = 1000). The total entropy generation (S-total) also increases with Pr due to an increase in S-psi Pr. It is found that, high heat transfer rate ((Nu(b)) over bar) and minimum entropy generation (S-total) occur for square cavities at Ra = 105 for all Pr in case 1. It is observed that S-total is smaller for case 1 compared to case 2, even though high (Nu(b)) over bar is observed at case 2 for all psi s. The inclination angle (phi) has almost identical effect on entropy production rate for 45 degrees <= phi <= 60 degrees within the entire range of Pr at all Ra.